To the cynically tuned ear, two remarks by Los Angeles Councilman Eric Garcetti in recent days seem to suggest the perils of a mayoral candidacy dependent, at least in some measure, on support from United Teachers Los Angeles, the union that represents local teachers.

The first came in a debate moderated by former Deputy Mayor Austin Beutner, who had considered running for mayor himself. Beutner tried to pin down Garcetti about whom the councilman is supporting in a school board race that features incumbent Monica Garcia, generally regarded as a supporter of reform, against four opponents, three of whom are backed by the union. "I admire Monica Garcia a lot," Garcetti said. Asked again whether that meant he would vote for her, Garcetti again responded: "I admire Monica Garcia a lot."

The second came in telling exchanges involving the so-called parent trigger law, which allows parents at a failing school to band together and force a district to demand changes, including to personnel. This time, it began with Patrick Range McDonald from LA Weekly, who posed a question to all five candidates, asking whether they supported the law, which the union opposes. Four said they did. Garcetti expressed support for parents who were turning to the law for help but stopped short of endorsing it outright.

Later, in an interview with me, he kept to that distinction. "I just don't think that it, by itself, turns a school around," he said. "We need systemic improvement."

There are plenty of reasons to be guarded about support for Garcia — my colleagues on The Times' editorial board endorsed her after first proclaiming that they considered her a "poor choice." And Garcetti raises legitimate concerns about the parent trigger law, which provides desperate parents with a tool for forcing change but doesn't address larger issues of district management.

Still, it's hard to regard Garcetti's wariness on these subjects as unrelated to his endorsement by UTLA, which has too often elevated job protection for teachers over the best interests of children.

Garcetti's principal rival, City Controller Wendy Greuel, backs the parent trigger law wholeheartedly, arguing that one of the frustrations parents feel toward schools is that they are denied influence and choices. The parent trigger supplies that, she said.

"Will there be growing pains? Absolutely," she said, adding that she is the only candidate in the field who has a child in Los Angeles public schools. "But does that mean you don't try? Absolutely not."

Even with their differences, there is much overlap in the positions of Garcetti and Greuel on education. Indeed, most of the candidates for mayor — including Councilwoman Jan Perry, lawyer and former prosecutor Kevin James and young businessman and activist Emanuel Pleitez — have hammered on the importance of education. Pleitez in particular has made it a centerpiece of his candidacy, proclaiming over and over that a mayor should focus on that issue "24/7."

All of the candidates have said the mayor should do more to bring resources to public schools and use the power of the office to focus on the problems of schools. Beyond that, Garcetti talks of using the city to "leverage" private money and support, and to use city and federal money more creatively — directing block grants, for instance, to facilitate the housing of more community centers in schools. Greuel emphasizes her collaboration with LAUSD Supt. John Deasy and her work with her own son's L.A. Unified-affiliated charter school.

It was once easy for city candidates to sidestep education, over which the mayor has no formal authority. Then came Mayors Richard Riordan and Antonio Villaraigosa, both of whom demonstrated ways that the mayor could stake a serious political claim on the issue. Today, a mayor is expected to help schools.

Indeed, just last week brought a reminder of the importance of a mayor on an issue he doesn't control directly. When parents at 24th Street Elementary School filed their petition under the parent trigger law, they had every reason to expect that the school board would fight them just as school boards, backed by unions, have done elsewhere in the state. Instead, the board, with Villaraigosa leading a chorus of support for the parents, cheerfully accepted the petition. That's an example of how mayors can wield influence on education issues.

On Wednesday, the mayoral candidates, entering their final week before the first round of the election, will have an opportunity to further illuminate their ideas on education during a panel discussion devoted to the issue. Garcetti should also take the opportunity to lay to rest fears that his positions have been molded by his UTLA support.